Analysis of x 7→ 1 − x2 ex
Warning: some values are approximated. Some results may be wrong .
We consider the function defined by f (x) = 1 − x2 ex .
We narrow the analysis down to ]−∞ ;0 ].
It is derivable on ]−∞ ;0 ].
Its derivative is f 0 (x) = −x (x + 2) ex .
It admits the below limit:
lim f (x) = 1
x→−∞
The equation of its horizontal asymptote is:
y=1
A table of values is:
x
f (x)
−2
1 − 4 · e−2 ≈ 0.458
0
1
Its table of variations is:
x
−∞
f 0 (x)
f (x) 1
−2
−
0
0
+ 0
1
& 1 − 4 · e−2 %
Its table of signs is:
x −∞
f (x)
0
+
Its graph is:
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Note: these results have been obtained from an automated program and are not guaranteed to be
exact.
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